397
Views
43
CrossRef citations to date
0
Altmetric
Original Articles

Free material optimization: recent progressFootnote

, &
Pages 79-100 | Received 02 Oct 2006, Accepted 03 Apr 2007, Published online: 27 Oct 2009

References

  • Achtziger , W and Kanzow , Ch . November 2005 . Mathematical programs with vanishing constraints: Optimality conditions and constraint qualifications , November , Germany : Institute of Applied Mathematics and Statistics, University of Würzburg . Technical Report No. 263
  • Ben-Tal , A , Kočvara , M , Nemirovski , A and Zowe , J . 1997 . Free material design via semidefinite programming. The multi-load case with contact conditions . SIAM J. Optim. , 9 : 813 – 832 .
  • Bendsøe , M and Sigmund , O . 2002 . Topology Optimization. Theory, Methods and Applications , Heidelberg : Springer-Verlag .
  • Bendsøe , MP , Guades , JM , Haber , RB , Pedersen , P and Taylor , JE . 1994 . An analytical model to predict optimal material properties in the context of optimal structural design . J. Appl. Mech. , 61 : 930 – 937 .
  • Breitfeld , M and Shanno , D . 1994 . A globally convergent penalty-barrier algorithm for nonlinear programming and its computational performance , New Jersey : Technical report, Rutcor Research Report, Rutgers University .
  • Ciarlet , PG . 1978 . The Finite Element Method for Elliptic Problems , Amsterdam, New York, Oxford : North-Holland .
  • Duff , IS and Reid , JK . 1982 . MA 27—A set of Fortran subroutines for solving sparse symmetric sets of linear equations , Harwell, Oxfordshire, , UK : Tech. Report R.10533, AERE .
  • Kočvara , M , Leibfritz , F , Stingl , M and Henrion , D . 2004 . A nonlinear SDP algorithm for static output feedback problems in COMPlib , LAAS-CNRS research report no. 04508 Toulouse : LAAS .
  • Kočvara , M and Stingl , M . 2003 . PENNON—a code for convex nonlinear and semidefinite programming . Optim. Methods Software , 18 ( 3 ) : 317 – 333 .
  • Kočvara , M and Stingl , M . 2004 . Solving nonconvex sdp problems of structural optimization with stability control . Optim. Methods Software , 19 ( 5 ) : 595 – 609 .
  • Kočvara , M and Stingl , M . 2006 . On the solution of large-scale SDP problems by the modified barrier method using iterative solvers . Math. Program., Ser. B , 109 doi: 10.1007/s10107-006-0029-9
  • Kočvara , M and Zowe , J . 2002 . “ Free material optimization: An overview ” . In Trends in Industrial and Applied Mathematics , Edited by: Siddiqi , A.H. and Kočvara , M. 181 – 215 . Dordrecht : Kluwer Academic Publishers .
  • Mittelmann , H . Benchmarks for optimization software , as of 26 November 2005. Available at http://plato.la.asu.edu/bench.html
  • Polyak , R . 1992 . Modified barrier functions: Theory and methods . Math. Program. , 54 : 177 – 222 .
  • Ringertz , U . 1993 . On finding the optimal distribution of material properties . Struct. Optim. , 5 : 265 – 267 .
  • Stingl , M . 2005 . On the Solution of Nonlinear Semidefinite Programs by Augmented Lagrangian Methods, PhD thesis , Erlangen, , Germany : Institute of Applied Mathematics II, Friedrich-Alexander University of Erlangen-Nuremberg .
  • Sturm , J . 1999 . Optim. Methods Software, 11 and 12 . Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones , : 625 – 653 . Available at http://fewcal.kub.nl/sturm/
  • Vanderbei , RJ and Shanno , DF . 1999 . An interior point algorithm for nonconvex nonlinear programming . Comput. Optim. Appl. , 13 : 231 – 252 .
  • Wächter , A and Biegler , LT . 2006 . On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming . Math. Program. , 106 : 25 – 57 .
  • Werner , R . 2000 . Free Material Optimization. Mathematical Analysis and Numerical Solution, PhD thesis , Erlangen, , Germany : Inst. of Applied Mathematics, University of Erlangen .
  • Zowe , J , Kočvara , M and Bendsøe , M . 1997 . Free material optimization via mathematical programming . Math. Program., Ser. B , 79 : 445 – 466 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.